She is best remembered as the housekeeper on the television series, The Ghost & Mrs. Muir. She earlier appeared in the first season (1958–1959) of CBS's The Ann Sothern Show in the role of Flora Macauley, the overbearing wife of the gentlemanly hotel owner Jason Macauley, played by Ernest Truex.

Shaw's character of Bertha/Hagatha, a matronly witch, was a recurring role on TV's Bewitched. She also appeared as Miss Gormley in an episode of NBC's The Brian Keith Show. She played escaped convict Big Maude Tyler in an episode of CBS's The Andy Griffith Show, entitled "Convicts at Large". She appeared again in season four as Eleanora Poultice, the educated voice teacher of the legendary Barney Fife. In 1965, he guest starred in season 1 episode 15 ["Return from Outer Space"] of "Lost In Space" as Aunt Clara. In ABC's The Odd Couple, she appeared as a housekeeper who was a former army colonel. Shaw also appeared in an episode in season 4 of I Dream of Jeannie entitled "Jeannie and the Wild Pipchicks", in which she played a strict dietician who has her innermost inhibition released (in her case a beautiful butterfly).

In 1973 she played a country nurse, Ozella Peterson, in the Emergency! episode "Snakebite." In 1966 she played Aunt Clara on a 'Lost In Space' episode from the first season titled, 'Return From Outer Space.' This is the episode where young Will Robinson actually gets back to Earth but nobody believes he is really who he says he is.